Long memory characteristic of volatility based on stable distribution

Based on stable distributions of time series generating process, we study the relationship between the skewness and fat tail of distribution of high frequency data and long memory of the realized volatility constructed from the data respectively. Simulation results indicate that without noise participating in data, there is not obvious relation between the skewness and fat tail of the distribution of time series and long memory of volatility of the time series. Meanwhile, the changes of sampling interval have little effect on the relationship between them.